Question: Solve for $x$ and $y$ using elimination. ${2x-2y = 12}$ ${-2x+5y = -3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {2x-2y = 12}\thinspace$ to find $x$ ${2x - 2}{(3)}{= 12}$ $2x-6 = 12$ $2x-6{+6} = 12{+6}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 3}$ into $\thinspace {-2x+5y = -3}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(3)}{= -3}$ ${x = 9}$